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<h1 class="reftitle">EMinTimeController</h1>
<h2>Purpose</h2>
<p>Explicit minimum-time MPC controller</p>
<h2>Syntax</h2>
<pre class="synopsis">ctrl = EMinTimeController(model)</pre>
<h2>Description</h2>
<p></p> 
    Constructs the explicit form of a minimum-time MPC controller by
    solving the following optimization problem parametrically:
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller9.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller9.png"></p>
    where <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller1.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller1.png"> represents the prediction model's
    state-update equation, <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller2.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller2.png"> is a given terminal set, and 
    <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller3.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller3.png"> and <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller4.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller4.png"> denote, respectively, the state and input
    constraints.<br><br>

    LTI, PWA, and MLD models are accepted for predictions.
    State and input constraint sets <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller5.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller5.png">, <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller6.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller6.png"> are
    automatically created using the model's state and input
    constraints (<tt>model.x.min</tt>, <tt>model.x.max</tt>,
    <tt>model.u.min</tt>, <tt>model.u.max</tt>). The terminal set
    <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller7.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller7.png"> is either taken from <tt>model.x.terminalSet</tt>
    or, if the field is empty, by calling
    <tt>model.stabizilingController()</tt> (for LTI systems only).<br><br>

    Once computed, explicit minimum-time controllers inherit the
    behavior of the <tt>EMPCController</tt> class in terms of internal
    structure, evaluation and post-processing. See "<tt>help
    EMPCController</tt>" for more details.
  <h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
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<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>model</tt></td>
<td>
<p></p>Prediction model<p>
	    		Class: <tt>AbstractSystem</tt></p>
</td>
</tr></tbody>
</table>
<h2>Output Arguments</h2>
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<td><tt>ctrl</tt></td>
<td>
<p></p>Explicit minimum-time controller.<p>
	    		Class: <tt>EMinTimeController</tt></p>
</td>
</tr></tbody>
</table>
<h2>Example(s)</h2>
<h3>Example 
				1</h3>Create a 1D LTI system<pre class="programlisting">sys = LTISystem('A', 1, 'B', 1, 'C', 1, 'D', 0)</pre>
<pre class="programlisting">LTISystem with 1 state, 1 input, 1 output
</pre>Define constraints and quadratic cost function with unity weights<pre class="programlisting">
		sys.x.min = -1; sys.x.max = 1;
		sys.u.min = -1; sys.u.max = 1;
		sys.x.penalty = QuadFunction(1);
		sys.u.penalty = QuadFunction(1);
	</pre>
<pre class="programlisting"></pre>Define a terminal set <img src="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller8.png" alt="../../../../../fig/mpt/modules/ui/@EMinTimeController/emintimecontroller8.png"> and construct the explicit minimum-time controller<pre class="programlisting">
		sys.x.with('terminalSet');
		sys.x.terminalSet = Polyhedron('lb', -0.1, 'ub', 0.1);
		ctrl = EMinTimeController(sys)
	</pre>
<pre class="programlisting">Using provided terminal state set...
Iterating...
New horizon: 1
mpt_plcp: 3 regions
New horizon: 2
mpt_plcp: 1 regions
Explicit minimum-time controller (horizon: 1, regions: 4, partitions: 2)
</pre>
<h2>See Also</h2>mintimecontrollerr, <a href="../@EMPCController/empccontroller.html">empccontroller</a><p></p>
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<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
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